products “in stock” at the beginning of the list

Use a relevanssi_hits_filter sorting function. Here’s some examples.

You just have to check each post for their product_visibility taxonomy terms. If the post doesn’t have any, it’s in stock, and needs to be sorted that way.

Thank you, but I could not understand which of the examples would suit me. You can send me a code that I can add to the functions

The “Sorting by category” is the closest one, since category and product_visibility are both taxonomies.

If this is something you can’t do yourself, any skilled WP developer should find this a small and easy task to do. It shouldn’t be too expensive to hire someone to do it for you.